Cosmic Time, Energy Density, and the Age of the Universe

Standard cosmology estimates the age of the universe by assuming a globally uniform flow of cosmic time and extrapolating the FLRW scale factor backward under this assumption. This procedure leads to the conclusion that the universe must have originated from a vanishing scale factor, producing the Big Bang singularity. In this work we challenge the assumption of constant cosmic time by introducing an energy-dependent time rate motivated by relativistic considerations. Earlier studies showed that relativistic effects can be expressed more fundamentally as functions of energy rather than velocity, that spatial volume encodes energy content, and that energy density varies exponentially with the radius of a region. Combining these results, we argue that the early universe, having extremely high energy density and extremely small volume, must have experienced strong relativistic time dilation, causing the physical rate of time to slow dramatically. We construct a cosmological model in which the physical time variable τ satisfies dτ/dt = f(ρ) with f(ρ) → 0 at high energy density. The resulting physical Hubble parameter Hphys = Hstd/f(ρ) modifies the expansion history, eliminates the Big Bang singularity, and yields an infinite proper age for the universe even when the coordinate time remains finite. We show how this framework alters observable quantities such as luminosity distances, the CMB acoustic scale, and early-universe expansion constraints. The model provides a non-singular, past-eternal cosmology in which time, energy density, and spatial volume are dynamically linked.